The present invention uses a variable previously not used by petroleum geologists--the response of a reservoir to tidal forces.
The word "tide" generally invokes an image of a changing water level at a shoreline, but the moon and the sun also cause tides in the atmosphere, in the solid earth, and in reservoirs within the solid earth. The "earth-tide" is associated with a periodic dilation and constriction of the earth's crust. That dilation and constriction is caused both by the gravitational attraction of the earth to the moon and the sun (other celestial bodies being too far away to appreciably influence the earth) and by the changing weight loads caused by the water tide and atmospheric tide. The present invention is based in part on the fact that hydrocarbon reservoirs respond to this periodic deformation of the earth and to the forces that cause this periodic deformation.
By "earth-tide," we mean the periodic movement in the earth's crust caused by the gravitational attraction of the moon and the sun occuring unequally on different parts of the earth.
By "response of a reservoir to tidal forces," we mean the periodic movement of fluids within a reservoir caused by the same forces that produce the earth-tide at that location. Another name for this response is the "reservoir-tide".
To understand earth-tides and reservoir-tides, consider the sun-earth system and the earth-moon system in isolation, shown in FIGS. 1 and 2.
Referring to FIG. 1, the center of the earth (C) travels at a constant linear velocity in its orbit around the sun. This constant linear velocity is exactly the magnitude required to maintain an orbit. Since both centrifugal force and linear velocity vary proportionally to the distance from the center of rotation, the point (N) on earth nearest the sun has less centrifugal force, and less linear velocity, than at the center of the earth and thus will tend to move toward the sun. The point (F) on the far side of the earth has more centrifugal force, and more linear velocity, and thus will tend to move away from the sun.
Referring to FIG. 2, the earth and the moon rotate about a common axis (A), contained within the earth. A point (N') on the side of the earth nearest the moon experiences a greater gravitational attraction than a point on the common axis. Point N' also experiences an outward normal acceleration due to its rotation about the common axis and this acceleration has a positive component directed toward the moon. A point (F') on the side of the earth farthest from the moon has less gravitational attraction to the moon and has a positive component of centrifugal acceleration directed away from the moon.
Thus the movement of earth in orbit around the sun and the movement of the moon around the earth have similar consequences but for different reasons. Each phenomenon contributes to symmetric bulges on opposite sides of the earth. The observed tidal deformation of the earth is the complex superposition of these two pairs of bulges.
The earth-tide can be observed by the type of standard gravity meter used in hydrocarbon and minerals exploration. Such a gravity meter can define the earth-tide's smooth regularity. The earth-tide's dominant periodicity is approximately twelve hours.
Table A lists the major known components that combine to form the observable earth-tide. Note that the influence of the moon is about twice that of the sun.
TABLE A ______________________________________ Known components of the earth-tide Common Component Realtive Symbol Name Period Amplitude ______________________________________ M.sub.2 principal lunar 12.42 hr 0.454 S.sub.2 principal solar 12.00 hr 0.212 N.sub.2 larger lunar elliptic 12.66 hr 0.088 K.sub.2 lunisolar 11.97 hr 0.058 K.sub.1 lunisolar 23.93 hr 0.266 O.sub.1 larger lunar 25.82 hr 0.189 P.sub.1 larger solar 24.07 hr 0.088 M.sub.f lunar fortnightly 13.66 days 0.078 S.sub.sa solar semi-annual 1/2 year 0.037 nineteen yearly 19 years 0.033 ______________________________________
Gravity changes are measured in gals (1 gal=1 cm/sec.sup.2). The useful unit for tidal gravity measurements is the microgal, which is one-millionth of a gal. One microgal is roughly one-billionth of the vertical component of the earth's gravity field. The total range of earth-tide induced gravity is within the limits of +300 microgals to -300 microgals.
In shallow aquifers the earth-tide manifests itself as a small periodic rise and fall of the water levels in wells. The relationship between the changing water levels and the changing position of the moon was recognized as early as the first century A.D. by Pliny the Elder. Compared to the minute (a few parts in 10.sup.8) dilation or constriction of the earth's crust, the rise and fall of the water level is usually at least a few centimeters. This same effect occurs in hydrocarbon reservoirs.
The observed amplitudes of earth-tide are about twenty percent larger than those predicted from the rigid-earth theory. For a given location, this magnification appears to be a constant and is called the "gravity magnification factor."
The variations in the water-tide also influence the hydrocarbon reservoir. This is because there is more water above the reservoir at high-tide than at low tide.
The variations in the atmospheric tide are difficult to measure because they are much smaller than either the earth-tide or the water-tide, but they also influence the hydrocarbon reservoir. The atmosphere is a load on the surface of the entire earth in the same way that the oceans are loads on the ocean-bottom.